Imaging science may be naturally divided into the process of image formation, the use of data from sensors to form images, and of image interpretation,
the extraction of information from images. The IMA annual program has been organized along these lines, although we fully realize the interconnectedness of the image
formation and interpretation process, and intend to encourage an interplay between them. In particular, the spring semester will begin with a period of concentration
in image processing, which straddles the divisions.

Many classical and well-developed imaging techniques use wave propagation to generate data. Recently, rapid developments in sensor technology coupled with advances in
mathematics for integrating the collected data, promise to provide quantitative imaging information about structures and phenomena long assumed to be inaccessible to
imaging. Examples in these emerging areas include in vivo cell imaging, quantum state imaging, and network tomography. The development of imaging techniques together
with the advancement of image processing methods have called for intelligent integration of these subsystems.

Full Description

The process of image understanding usually begins with the storage, enhancement, and transmission of existing images. Image understanding also involves the extraction
of certain features and information from the often overwhelming stream of information produced by the above imaging techniques. While this is often considered to be
part of electrical engineering and computer science, it is highly mathematical and mathematics has had a major role in much of the recent progress in this field.
As in all most interdisciplinary efforts, the push has occured in many ways. For example, the analysis of "shape" has driven research in differential geometry,
stochastic diffusions and nonlinear partial differential equations.

Bayesian modeling and inference is based on the observation that natural images, whereas notoriously ambiguous at a local level, are perceived globally as largely
unambiguous due to incorporating pre-observation and post-observation likelihoods. Special cases such as deformable templates and compositional vision lead
to the construction of probability measures on complex structures, such as grammars, graphs and spaces of transformations and numerous mathematical questions
arise in learning representations from data ("statistical learning"). The simple observation that the names of objects do not change under various image
transformations has led to another approach to image interpretation based on "invariant" functionals--photometric, geometric and algebraic. Finally, nearly all
methods encounter formidable computational challenges, inspiring new strategies for simulation, search and optimization.

Imaging science is highly interdisciplinary, naturally connecting mathematical sciences with a variety of application areas. Mathematical areas that have contributed
to this field include harmonic analysis, partial differential equations, and integral geometry, calculus of variations, probability theory, statistics, and learning
theory. Historically, interchange of ideas among researchers coming from different applications has been impeded by barriers of jargon and culture. By bringing
together a range of researchers and emphasizing the underlying mathematical structures and algorithms in the highly interdisciplinary atmosphere of the IMA, this
program is a great opportunity to significantly contribute to advances in imaging science.